Randall was born in Gering, Nebraska, the son of horse trainer George Randall, Sr. He was diagnosed with polio as a child, and his father made him exercise in place of the prescribed treatments of the day. By the age of 10, Corky was galloping thoroughbred colts for his father each morning before school.

Corky Randall began working at Republic Pictures during high school. He spent nearly a half century training and wrangling horses for Hollywood productions. Perhaps his best known work was on the 1979 family film The Black Stallion, which featured some of the most challenging horse stunts ever filmed. He also trained the horses in the 1983 sequel, The Black Stallion Returns. Teri Garr was among the stars of both films.

Randall was the recipient of two PATSY Awards and the 1982 Humanitarian Award from the Los Angeles chapter of the Society for the Prevention of Cruelty to Animals. He died of cancer in Newhall, California, at the age of 80.